Gauge invariance and pseudoperturbations

We define pseudoperturbations as the difference between two Hamiltonians that are related by a generalized gauge transformation. We state and prove the theorem that such pseudoperturbations cannot cause any real physical transitions. We also rigorously establish the generalized gauge invariance of physical transition-matrix elements in real processes. Our theorem also generates some interesting sum rules and onshell identities which can serve as useful constraints in variational calculations.